Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,6,Mod(67,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("147.67");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(23.5764215125\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} + 63 x^{10} - 126 x^{9} + 2784 x^{8} - 5290 x^{7} + 62015 x^{6} - 99530 x^{5} + \cdots + 5466244 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{8}\cdot 7^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 79.6 | ||
Root | \(-2.80572 - 4.85966i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.79 |
Dual form | 147.6.e.p.67.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.59404 | − | 9.68915i | 0.988895 | − | 1.71282i | 0.365743 | − | 0.930716i | \(-0.380815\pi\) |
0.623152 | − | 0.782101i | \(-0.285852\pi\) | |||||||
\(3\) | −4.50000 | − | 7.79423i | −0.288675 | − | 0.500000i | ||||
\(4\) | −46.5865 | − | 80.6901i | −1.45583 | − | 2.52157i | ||||
\(5\) | 31.1575 | − | 53.9664i | 0.557362 | − | 0.965380i | −0.440353 | − | 0.897825i | \(-0.645147\pi\) |
0.997716 | − | 0.0675552i | \(-0.0215199\pi\) | |||||||
\(6\) | −100.693 | −1.14188 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −684.407 | −3.78085 | ||||||||
\(9\) | −40.5000 | + | 70.1481i | −0.166667 | + | 0.288675i | ||||
\(10\) | −348.592 | − | 603.780i | −1.10235 | − | 1.90932i | ||||
\(11\) | 86.7474 | + | 150.251i | 0.216160 | + | 0.374400i | 0.953631 | − | 0.300979i | \(-0.0973134\pi\) |
−0.737471 | + | 0.675379i | \(0.763980\pi\) | |||||||
\(12\) | −419.278 | + | 726.211i | −0.840522 | + | 1.45583i | ||||
\(13\) | 348.244 | 0.571512 | 0.285756 | − | 0.958302i | \(-0.407755\pi\) | ||||
0.285756 | + | 0.958302i | \(0.407755\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −560.835 | −0.643587 | ||||||||
\(16\) | −2337.83 | + | 4049.24i | −2.28304 | + | 3.95434i | ||||
\(17\) | −499.603 | − | 865.338i | −0.419279 | − | 0.726212i | 0.576588 | − | 0.817035i | \(-0.304384\pi\) |
−0.995867 | + | 0.0908228i | \(0.971050\pi\) | |||||||
\(18\) | 453.117 | + | 784.821i | 0.329632 | + | 0.570939i | ||||
\(19\) | 1021.09 | − | 1768.57i | 0.648901 | − | 1.12393i | −0.334485 | − | 0.942401i | \(-0.608562\pi\) |
0.983386 | − | 0.181528i | \(-0.0581042\pi\) | |||||||
\(20\) | −5806.07 | −3.24569 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1941.07 | 0.855038 | ||||||||
\(23\) | 974.835 | − | 1688.46i | 0.384248 | − | 0.665537i | −0.607417 | − | 0.794383i | \(-0.707794\pi\) |
0.991665 | + | 0.128846i | \(0.0411274\pi\) | |||||||
\(24\) | 3079.83 | + | 5334.43i | 1.09144 | + | 1.89043i | ||||
\(25\) | −379.079 | − | 656.585i | −0.121305 | − | 0.210107i | ||||
\(26\) | 1948.09 | − | 3374.19i | 0.565166 | − | 0.978896i | ||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 738.129 | 0.162981 | 0.0814906 | − | 0.996674i | \(-0.474032\pi\) | ||||
0.0814906 | + | 0.996674i | \(0.474032\pi\) | |||||||
\(30\) | −3137.33 | + | 5434.02i | −0.636440 | + | 1.10235i | ||||
\(31\) | 1229.99 | + | 2130.41i | 0.229879 | + | 0.398162i | 0.957772 | − | 0.287529i | \(-0.0928337\pi\) |
−0.727893 | + | 0.685691i | \(0.759500\pi\) | |||||||
\(32\) | 15205.3 | + | 26336.4i | 2.62495 | + | 4.54654i | ||||
\(33\) | 780.727 | − | 1352.26i | 0.124800 | − | 0.216160i | ||||
\(34\) | −11179.2 | −1.65849 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 7547.01 | 0.970552 | ||||||||
\(37\) | −4393.26 | + | 7609.35i | −0.527573 | + | 0.913783i | 0.471911 | + | 0.881646i | \(0.343565\pi\) |
−0.999483 | + | 0.0321367i | \(0.989769\pi\) | |||||||
\(38\) | −11424.0 | − | 19786.9i | −1.28339 | − | 2.22290i | ||||
\(39\) | −1567.10 | − | 2714.30i | −0.164981 | − | 0.285756i | ||||
\(40\) | −21324.4 | + | 36935.0i | −2.10730 | + | 3.64996i | ||||
\(41\) | 17617.4 | 1.63675 | 0.818374 | − | 0.574686i | \(-0.194876\pi\) | ||||
0.818374 | + | 0.574686i | \(0.194876\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10317.1 | −0.850914 | −0.425457 | − | 0.904979i | \(-0.639887\pi\) | ||||
−0.425457 | + | 0.904979i | \(0.639887\pi\) | |||||||
\(44\) | 8082.51 | − | 13999.3i | 0.629383 | − | 1.09012i | ||||
\(45\) | 2523.76 | + | 4371.28i | 0.185787 | + | 0.321793i | ||||
\(46\) | −10906.5 | − | 18890.7i | −0.759962 | − | 1.31629i | ||||
\(47\) | 37.5291 | − | 65.0023i | 0.00247813 | − | 0.00429224i | −0.864784 | − | 0.502145i | \(-0.832545\pi\) |
0.867262 | + | 0.497852i | \(0.165878\pi\) | |||||||
\(48\) | 42081.0 | 2.63623 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −8482.34 | −0.479833 | ||||||||
\(51\) | −4496.43 | + | 7788.04i | −0.242071 | + | 0.419279i | ||||
\(52\) | −16223.5 | − | 28099.9i | −0.832023 | − | 1.44111i | ||||
\(53\) | −13852.8 | − | 23993.7i | −0.677403 | − | 1.17330i | −0.975760 | − | 0.218842i | \(-0.929772\pi\) |
0.298358 | − | 0.954454i | \(-0.403561\pi\) | |||||||
\(54\) | 4078.05 | − | 7063.39i | 0.190313 | − | 0.329632i | ||||
\(55\) | 10811.3 | 0.481917 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −18379.5 | −0.749286 | ||||||||
\(58\) | 4129.12 | − | 7151.85i | 0.161171 | − | 0.279157i | ||||
\(59\) | 1728.79 | + | 2994.35i | 0.0646564 | + | 0.111988i | 0.896542 | − | 0.442960i | \(-0.146072\pi\) |
−0.831885 | + | 0.554948i | \(0.812738\pi\) | |||||||
\(60\) | 26127.3 | + | 45253.9i | 0.936951 | + | 1.62285i | ||||
\(61\) | −7978.20 | + | 13818.6i | −0.274524 | + | 0.475490i | −0.970015 | − | 0.243045i | \(-0.921854\pi\) |
0.695491 | + | 0.718535i | \(0.255187\pi\) | |||||||
\(62\) | 27522.5 | 0.909304 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 190615. | 5.81711 | ||||||||
\(65\) | 10850.4 | − | 18793.5i | 0.318539 | − | 0.551726i | ||||
\(66\) | −8734.83 | − | 15129.2i | −0.246828 | − | 0.427519i | ||||
\(67\) | −7206.58 | − | 12482.2i | −0.196129 | − | 0.339706i | 0.751141 | − | 0.660142i | \(-0.229504\pi\) |
−0.947270 | + | 0.320436i | \(0.896171\pi\) | |||||||
\(68\) | −46549.5 | + | 80626.1i | −1.22079 | + | 2.11448i | ||||
\(69\) | −17547.0 | −0.443691 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −30337.6 | −0.714225 | −0.357112 | − | 0.934061i | \(-0.616239\pi\) | ||||
−0.357112 | + | 0.934061i | \(0.616239\pi\) | |||||||
\(72\) | 27718.5 | − | 48009.8i | 0.630142 | − | 1.09144i | ||||
\(73\) | −42940.5 | − | 74375.0i | −0.943104 | − | 1.63350i | −0.759504 | − | 0.650503i | \(-0.774558\pi\) |
−0.183600 | − | 0.983001i | \(-0.558775\pi\) | |||||||
\(74\) | 49152.1 | + | 85133.9i | 1.04343 | + | 1.80727i | ||||
\(75\) | −3411.71 | + | 5909.26i | −0.0700357 | + | 0.121305i | ||||
\(76\) | −190275. | −3.77875 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −35065.6 | −0.652597 | ||||||||
\(79\) | −3806.63 | + | 6593.27i | −0.0686234 | + | 0.118859i | −0.898296 | − | 0.439392i | \(-0.855194\pi\) |
0.829672 | + | 0.558251i | \(0.188527\pi\) | |||||||
\(80\) | 145682. | + | 252329.i | 2.54496 | + | 4.40800i | ||||
\(81\) | −3280.50 | − | 5681.99i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 98552.2 | − | 170697.i | 1.61857 | − | 2.80345i | ||||
\(83\) | 63725.4 | 1.01535 | 0.507677 | − | 0.861548i | \(-0.330504\pi\) | ||||
0.507677 | + | 0.861548i | \(0.330504\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −62265.5 | −0.934761 | ||||||||
\(86\) | −57714.1 | + | 99963.8i | −0.841465 | + | 1.45746i | ||||
\(87\) | −3321.58 | − | 5753.15i | −0.0470486 | − | 0.0814906i | ||||
\(88\) | −59370.6 | − | 102833.i | −0.817268 | − | 1.41555i | ||||
\(89\) | −23195.7 | + | 40176.1i | −0.310407 | + | 0.537641i | −0.978451 | − | 0.206481i | \(-0.933799\pi\) |
0.668043 | + | 0.744122i | \(0.267132\pi\) | |||||||
\(90\) | 56472.0 | 0.734897 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −181657. | −2.23759 | ||||||||
\(93\) | 11070.0 | − | 19173.7i | 0.132721 | − | 0.229879i | ||||
\(94\) | −419.878 | − | 727.251i | −0.00490122 | − | 0.00848916i | ||||
\(95\) | −63629.0 | − | 110209.i | −0.723345 | − | 1.25287i | ||||
\(96\) | 136848. | − | 237027.i | 1.51551 | − | 2.62495i | ||||
\(97\) | 21461.2 | 0.231592 | 0.115796 | − | 0.993273i | \(-0.463058\pi\) | ||||
0.115796 | + | 0.993273i | \(0.463058\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −14053.1 | −0.144107 | ||||||||
\(100\) | −35319.9 | + | 61175.9i | −0.353199 | + | 0.611759i | ||||
\(101\) | −72966.4 | − | 126382.i | −0.711737 | − | 1.23277i | −0.964205 | − | 0.265160i | \(-0.914575\pi\) |
0.252467 | − | 0.967605i | \(-0.418758\pi\) | |||||||
\(102\) | 50306.4 | + | 87133.2i | 0.478765 | + | 0.829245i | ||||
\(103\) | −82814.3 | + | 143439.i | −0.769152 | + | 1.33221i | 0.168871 | + | 0.985638i | \(0.445988\pi\) |
−0.938023 | + | 0.346572i | \(0.887346\pi\) | |||||||
\(104\) | −238341. | −2.16080 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −309972. | −2.67952 | ||||||||
\(107\) | −107524. | + | 186237.i | −0.907918 | + | 1.57256i | −0.0909669 | + | 0.995854i | \(0.528996\pi\) |
−0.816951 | + | 0.576707i | \(0.804338\pi\) | |||||||
\(108\) | −33961.5 | − | 58823.1i | −0.280174 | − | 0.485276i | ||||
\(109\) | 20232.0 | + | 35042.8i | 0.163107 | + | 0.282509i | 0.935981 | − | 0.352050i | \(-0.114515\pi\) |
−0.772875 | + | 0.634559i | \(0.781182\pi\) | |||||||
\(110\) | 60479.0 | − | 104753.i | 0.476566 | − | 0.825436i | ||||
\(111\) | 79078.7 | 0.609189 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15002.6 | −0.110528 | −0.0552638 | − | 0.998472i | \(-0.517600\pi\) | ||||
−0.0552638 | + | 0.998472i | \(0.517600\pi\) | |||||||
\(114\) | −102816. | + | 178082.i | −0.740965 | + | 1.28339i | ||||
\(115\) | −60746.9 | − | 105217.i | −0.428331 | − | 0.741890i | ||||
\(116\) | −34386.8 | − | 59559.7i | −0.237272 | − | 0.410968i | ||||
\(117\) | −14103.9 | + | 24428.7i | −0.0952521 | + | 0.164981i | ||||
\(118\) | 38683.6 | 0.255753 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 383840. | 2.43331 | ||||||||
\(121\) | 65475.3 | − | 113406.i | 0.406550 | − | 0.704165i | ||||
\(122\) | 89260.7 | + | 154604.i | 0.542951 | + | 0.940419i | ||||
\(123\) | −79278.2 | − | 137314.i | −0.472488 | − | 0.818374i | ||||
\(124\) | 114602. | − | 198497.i | 0.669328 | − | 1.15931i | ||||
\(125\) | 147490. | 0.844280 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 118326. | 0.650986 | 0.325493 | − | 0.945544i | \(-0.394470\pi\) | ||||
0.325493 | + | 0.945544i | \(0.394470\pi\) | |||||||
\(128\) | 579737. | − | 1.00413e6i | 3.12756 | − | 5.41710i | ||||
\(129\) | 46426.9 | + | 80413.7i | 0.245638 | + | 0.425457i | ||||
\(130\) | −121395. | − | 210263.i | −0.630004 | − | 1.09120i | ||||
\(131\) | 109733. | − | 190063.i | 0.558673 | − | 0.967650i | −0.438935 | − | 0.898519i | \(-0.644644\pi\) |
0.997608 | − | 0.0691309i | \(-0.0220226\pi\) | |||||||
\(132\) | −145485. | −0.726749 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −161256. | −0.775805 | ||||||||
\(135\) | 22713.8 | − | 39341.5i | 0.107264 | − | 0.185787i | ||||
\(136\) | 341932. | + | 592244.i | 1.58523 | + | 2.74570i | ||||
\(137\) | 71991.5 | + | 124693.i | 0.327702 | + | 0.567597i | 0.982056 | − | 0.188592i | \(-0.0603923\pi\) |
−0.654353 | + | 0.756189i | \(0.727059\pi\) | |||||||
\(138\) | −98158.7 | + | 170016.i | −0.438764 | + | 0.759962i | ||||
\(139\) | 244306. | 1.07250 | 0.536249 | − | 0.844060i | \(-0.319841\pi\) | ||||
0.536249 | + | 0.844060i | \(0.319841\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −675.524 | −0.00286150 | ||||||||
\(142\) | −169709. | + | 293945.i | −0.706293 | + | 1.22334i | ||||
\(143\) | 30209.3 | + | 52324.0i | 0.123538 | + | 0.213974i | ||||
\(144\) | −189364. | − | 327989.i | −0.761013 | − | 1.31811i | ||||
\(145\) | 22998.3 | − | 39834.1i | 0.0908395 | − | 0.157339i | ||||
\(146\) | −960842. | −3.73052 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 818666. | 3.07222 | ||||||||
\(149\) | 139885. | − | 242287.i | 0.516184 | − | 0.894057i | −0.483639 | − | 0.875267i | \(-0.660685\pi\) |
0.999823 | − | 0.0187896i | \(-0.00598127\pi\) | |||||||
\(150\) | 38170.5 | + | 66113.3i | 0.138516 | + | 0.239917i | ||||
\(151\) | 100209. | + | 173566.i | 0.357653 | + | 0.619474i | 0.987568 | − | 0.157190i | \(-0.0502436\pi\) |
−0.629915 | + | 0.776664i | \(0.716910\pi\) | |||||||
\(152\) | −698838. | + | 1.21042e6i | −2.45340 | + | 4.24941i | ||||
\(153\) | 80935.7 | 0.279519 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 153294. | 0.512503 | ||||||||
\(156\) | −146011. | + | 252899.i | −0.480369 | + | 0.832023i | ||||
\(157\) | −235001. | − | 407034.i | −0.760888 | − | 1.31790i | −0.942393 | − | 0.334507i | \(-0.891430\pi\) |
0.181505 | − | 0.983390i | \(-0.441903\pi\) | |||||||
\(158\) | 42588.8 | + | 73766.0i | 0.135723 | + | 0.235079i | ||||
\(159\) | −124675. | + | 215943.i | −0.391099 | + | 0.677403i | ||||
\(160\) | 1.89504e6 | 5.85218 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −73404.9 | −0.219754 | ||||||||
\(163\) | 293503. | − | 508362.i | 0.865253 | − | 1.49866i | −0.00154277 | − | 0.999999i | \(-0.500491\pi\) |
0.866796 | − | 0.498663i | \(-0.166176\pi\) | |||||||
\(164\) | −820732. | − | 1.42155e6i | −2.38282 | − | 4.12717i | ||||
\(165\) | −48651.0 | − | 84266.0i | −0.139118 | − | 0.240959i | ||||
\(166\) | 356482. | − | 617445.i | 1.00408 | − | 1.73911i | ||||
\(167\) | 172819. | 0.479513 | 0.239757 | − | 0.970833i | \(-0.422932\pi\) | ||||
0.239757 | + | 0.970833i | \(0.422932\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −250019. | −0.673374 | ||||||||
\(170\) | −348316. | + | 603300.i | −0.924380 | + | 1.60107i | ||||
\(171\) | 82707.9 | + | 143254.i | 0.216300 | + | 0.374643i | ||||
\(172\) | 480636. | + | 832486.i | 1.23878 | + | 2.14564i | ||||
\(173\) | 2545.03 | − | 4408.12i | 0.00646514 | − | 0.0111979i | −0.862775 | − | 0.505589i | \(-0.831275\pi\) |
0.869240 | + | 0.494391i | \(0.164609\pi\) | |||||||
\(174\) | −74324.2 | −0.186105 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −811204. | −1.97400 | ||||||||
\(177\) | 15559.1 | − | 26949.1i | 0.0373294 | − | 0.0646564i | ||||
\(178\) | 259515. | + | 449493.i | 0.613920 | + | 1.06334i | ||||
\(179\) | −121139. | − | 209819.i | −0.282587 | − | 0.489455i | 0.689434 | − | 0.724348i | \(-0.257859\pi\) |
−0.972021 | + | 0.234894i | \(0.924526\pi\) | |||||||
\(180\) | 235146. | − | 407285.i | 0.540949 | − | 0.936951i | ||||
\(181\) | −492254. | −1.11684 | −0.558422 | − | 0.829557i | \(-0.688593\pi\) | ||||
−0.558422 | + | 0.829557i | \(0.688593\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 143608. | 0.316993 | ||||||||
\(184\) | −667184. | + | 1.15560e6i | −1.45278 | + | 2.51630i | ||||
\(185\) | 273766. | + | 474177.i | 0.588099 | + | 1.01862i | ||||
\(186\) | −123851. | − | 214517.i | −0.262494 | − | 0.454652i | ||||
\(187\) | 86678.6 | − | 150132.i | 0.181262 | − | 0.313956i | ||||
\(188\) | −6993.40 | −0.0144309 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.42377e6 | −2.86125 | ||||||||
\(191\) | 101865. | − | 176435.i | 0.202041 | − | 0.349946i | −0.747145 | − | 0.664661i | \(-0.768576\pi\) |
0.949186 | + | 0.314716i | \(0.101909\pi\) | |||||||
\(192\) | −857768. | − | 1.48570e6i | −1.67925 | − | 2.90855i | ||||
\(193\) | 30530.2 | + | 52879.8i | 0.0589979 | + | 0.102187i | 0.894016 | − | 0.448035i | \(-0.147876\pi\) |
−0.835018 | + | 0.550223i | \(0.814543\pi\) | |||||||
\(194\) | 120055. | − | 207941.i | 0.229021 | − | 0.396675i | ||||
\(195\) | −195308. | −0.367818 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 457733. | 0.840325 | 0.420162 | − | 0.907449i | \(-0.361973\pi\) | ||||
0.420162 | + | 0.907449i | \(0.361973\pi\) | |||||||
\(198\) | −78613.5 | + | 136163.i | −0.142506 | + | 0.246828i | ||||
\(199\) | 135274. | + | 234301.i | 0.242148 | + | 0.419412i | 0.961326 | − | 0.275414i | \(-0.0888148\pi\) |
−0.719178 | + | 0.694826i | \(0.755481\pi\) | |||||||
\(200\) | 259445. | + | 449371.i | 0.458638 | + | 0.794384i | ||||
\(201\) | −64859.3 | + | 112340.i | −0.113235 | + | 0.196129i | ||||
\(202\) | −1.63271e6 | −2.81533 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 837891. | 1.40965 | ||||||||
\(205\) | 548913. | − | 950746.i | 0.912261 | − | 1.58008i | ||||
\(206\) | 926532. | + | 1.60480e6i | 1.52122 | + | 2.63483i | ||||
\(207\) | 78961.7 | + | 136766.i | 0.128083 | + | 0.221846i | ||||
\(208\) | −814137. | + | 1.41013e6i | −1.30478 | + | 2.25995i | ||||
\(209\) | 354306. | 0.561065 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 933127. | 1.44289 | 0.721447 | − | 0.692469i | \(-0.243477\pi\) | ||||
0.721447 | + | 0.692469i | \(0.243477\pi\) | |||||||
\(212\) | −1.29070e6 | + | 2.23556e6i | −1.97236 | + | 3.41623i | ||||
\(213\) | 136519. | + | 236458.i | 0.206179 | + | 0.357112i | ||||
\(214\) | 1.20299e6 | + | 2.08364e6i | 1.79567 | + | 3.11019i | ||||
\(215\) | −321454. | + | 556775.i | −0.474267 | + | 0.821455i | ||||
\(216\) | −498933. | −0.727625 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 452713. | 0.645182 | ||||||||
\(219\) | −386464. | + | 669375.i | −0.544501 | + | 0.943104i | ||||
\(220\) | −503662. | − | 872368.i | −0.701588 | − | 1.21519i | ||||
\(221\) | −173984. | − | 301349.i | −0.239623 | − | 0.415039i | ||||
\(222\) | 442369. | − | 766205.i | 0.602424 | − | 1.04343i | ||||
\(223\) | −197037. | −0.265329 | −0.132664 | − | 0.991161i | \(-0.542353\pi\) | ||||
−0.132664 | + | 0.991161i | \(0.542353\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 61410.9 | 0.0808703 | ||||||||
\(226\) | −83925.2 | + | 145363.i | −0.109300 | + | 0.189314i | ||||
\(227\) | 599193. | + | 1.03783e6i | 0.771795 | + | 1.33679i | 0.936578 | + | 0.350458i | \(0.113974\pi\) |
−0.164784 | + | 0.986330i | \(0.552693\pi\) | |||||||
\(228\) | 856238. | + | 1.48305e6i | 1.09083 | + | 1.88937i | ||||
\(229\) | 122034. | − | 211370.i | 0.153778 | − | 0.266351i | −0.778836 | − | 0.627228i | \(-0.784189\pi\) |
0.932613 | + | 0.360877i | \(0.117523\pi\) | |||||||
\(230\) | −1.35928e6 | −1.69430 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −505181. | −0.616207 | ||||||||
\(233\) | 76130.2 | − | 131861.i | 0.0918686 | − | 0.159121i | −0.816429 | − | 0.577446i | \(-0.804049\pi\) |
0.908297 | + | 0.418325i | \(0.137383\pi\) | |||||||
\(234\) | 157795. | + | 273310.i | 0.188389 | + | 0.326299i | ||||
\(235\) | −2338.63 | − | 4050.62i | −0.00276243 | − | 0.00478467i | ||||
\(236\) | 161076. | − | 278992.i | 0.188257 | − | 0.326071i | ||||
\(237\) | 68519.3 | 0.0792395 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.51074e6 | 1.71078 | 0.855390 | − | 0.517984i | \(-0.173317\pi\) | ||||
0.855390 | + | 0.517984i | \(0.173317\pi\) | |||||||
\(240\) | 1.31114e6 | − | 2.27096e6i | 1.46933 | − | 2.54496i | ||||
\(241\) | −116469. | − | 201731.i | −0.129172 | − | 0.223733i | 0.794184 | − | 0.607678i | \(-0.207899\pi\) |
−0.923356 | + | 0.383945i | \(0.874565\pi\) | |||||||
\(242\) | −732542. | − | 1.26880e6i | −0.804070 | − | 1.39269i | ||||
\(243\) | −29524.5 | + | 51137.9i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 1.48670e6 | 1.59864 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.77394e6 | −1.86897 | ||||||||
\(247\) | 355587. | − | 615895.i | 0.370855 | − | 0.642339i | ||||
\(248\) | −841817. | − | 1.45807e6i | −0.869138 | − | 1.50539i | ||||
\(249\) | −286764. | − | 496690.i | −0.293107 | − | 0.507677i | ||||
\(250\) | 825063. | − | 1.42905e6i | 0.834905 | − | 1.44610i | ||||
\(251\) | 762727. | 0.764161 | 0.382081 | − | 0.924129i | \(-0.375208\pi\) | ||||
0.382081 | + | 0.924129i | \(0.375208\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 338258. | 0.332236 | ||||||||
\(254\) | 661921. | − | 1.14648e6i | 0.643757 | − | 1.11502i | ||||
\(255\) | 280195. | + | 485312.i | 0.269842 | + | 0.467380i | ||||
\(256\) | −3.43630e6 | − | 5.95185e6i | −3.27711 | − | 5.67612i | ||||
\(257\) | −690559. | + | 1.19608e6i | −0.652181 | + | 1.12961i | 0.330412 | + | 0.943837i | \(0.392812\pi\) |
−0.982593 | + | 0.185773i | \(0.940521\pi\) | |||||||
\(258\) | 1.03885e6 | 0.971640 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2.02193e6 | −1.85495 | ||||||||
\(261\) | −29894.2 | + | 51778.3i | −0.0271635 | + | 0.0470486i | ||||
\(262\) | −1.22770e6 | − | 2.12643e6i | −1.10494 | − | 1.91381i | ||||
\(263\) | 316805. | + | 548723.i | 0.282425 | + | 0.489174i | 0.971981 | − | 0.235058i | \(-0.0755279\pi\) |
−0.689557 | + | 0.724232i | \(0.742195\pi\) | |||||||
\(264\) | −534335. | + | 925496.i | −0.471850 | + | 0.817268i | ||||
\(265\) | −1.72647e6 | −1.51023 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 417522. | 0.358427 | ||||||||
\(268\) | −671459. | + | 1.16300e6i | −0.571061 | + | 0.989106i | ||||
\(269\) | 10266.9 | + | 17782.7i | 0.00865081 | + | 0.0149836i | 0.870318 | − | 0.492489i | \(-0.163913\pi\) |
−0.861668 | + | 0.507473i | \(0.830580\pi\) | |||||||
\(270\) | −254124. | − | 440155.i | −0.212147 | − | 0.367449i | ||||
\(271\) | 1.10469e6 | − | 1.91339e6i | 0.913732 | − | 1.58263i | 0.104984 | − | 0.994474i | \(-0.466521\pi\) |
0.808747 | − | 0.588156i | \(-0.200146\pi\) | |||||||
\(272\) | 4.67195e6 | 3.82892 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.61089e6 | 1.29625 | ||||||||
\(275\) | 65768.3 | − | 113914.i | 0.0524427 | − | 0.0908334i | ||||
\(276\) | 817454. | + | 1.41587e6i | 0.645938 | + | 1.11880i | ||||
\(277\) | 339920. | + | 588759.i | 0.266181 | + | 0.461039i | 0.967872 | − | 0.251442i | \(-0.0809047\pi\) |
−0.701691 | + | 0.712481i | \(0.747571\pi\) | |||||||
\(278\) | 1.36665e6 | − | 2.36711e6i | 1.06059 | − | 1.83699i | ||||
\(279\) | −199259. | −0.153253 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −831855. | −0.628466 | −0.314233 | − | 0.949346i | \(-0.601747\pi\) | ||||
−0.314233 | + | 0.949346i | \(0.601747\pi\) | |||||||
\(282\) | −3778.91 | + | 6545.26i | −0.00282972 | + | 0.00490122i | ||||
\(283\) | −1.15536e6 | − | 2.00114e6i | −0.857531 | − | 1.48529i | −0.874277 | − | 0.485427i | \(-0.838664\pi\) |
0.0167465 | − | 0.999860i | \(-0.494669\pi\) | |||||||
\(284\) | 1.41332e6 | + | 2.44794e6i | 1.03979 | + | 1.80097i | ||||
\(285\) | −572661. | + | 991877.i | −0.417624 | + | 0.723345i | ||||
\(286\) | 675968. | 0.488665 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.46326e6 | −1.74996 | ||||||||
\(289\) | 210722. | − | 364981.i | 0.148411 | − | 0.257055i | ||||
\(290\) | −257306. | − | 445667.i | −0.179662 | − | 0.311183i | ||||
\(291\) | −96575.3 | − | 167273.i | −0.0668550 | − | 0.115796i | ||||
\(292\) | −4.00089e6 | + | 6.92974e6i | −2.74599 | + | 4.75620i | ||||
\(293\) | 1.54768e6 | 1.05321 | 0.526603 | − | 0.850111i | \(-0.323465\pi\) | ||||
0.526603 | + | 0.850111i | \(0.323465\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 215459. | 0.144148 | ||||||||
\(296\) | 3.00678e6 | − | 5.20789e6i | 1.99468 | − | 3.45488i | ||||
\(297\) | 63238.9 | + | 109533.i | 0.0416000 | + | 0.0720533i | ||||
\(298\) | −1.56504e6 | − | 2.71073e6i | −1.02090 | − | 1.76826i | ||||
\(299\) | 339481. | − | 587998.i | 0.219602 | − | 0.380363i | ||||
\(300\) | 635759. | 0.407840 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2.24228e6 | 1.41473 | ||||||||
\(303\) | −656698. | + | 1.13743e6i | −0.410922 | + | 0.711737i | ||||
\(304\) | 4.77425e6 | + | 8.26925e6i | 2.96293 | + | 5.13195i | ||||
\(305\) | 497162. | + | 861109.i | 0.306019 | + | 0.530040i | ||||
\(306\) | 452757. | − | 784198.i | 0.276415 | − | 0.478765i | ||||
\(307\) | 149665. | 0.0906303 | 0.0453151 | − | 0.998973i | \(-0.485571\pi\) | ||||
0.0453151 | + | 0.998973i | \(0.485571\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.49066e6 | 0.888140 | ||||||||
\(310\) | 857534. | − | 1.48529e6i | 0.506812 | − | 0.877824i | ||||
\(311\) | 73243.5 | + | 126862.i | 0.0429406 | + | 0.0743753i | 0.886697 | − | 0.462351i | \(-0.152994\pi\) |
−0.843756 | + | 0.536726i | \(0.819661\pi\) | |||||||
\(312\) | 1.07253e6 | + | 1.85768e6i | 0.623770 | + | 1.08040i | ||||
\(313\) | −159167. | + | 275686.i | −0.0918319 | + | 0.159057i | −0.908282 | − | 0.418359i | \(-0.862606\pi\) |
0.816450 | + | 0.577416i | \(0.195939\pi\) | |||||||
\(314\) | −5.25842e6 | −3.00975 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 709349. | 0.399615 | ||||||||
\(317\) | −1.08296e6 | + | 1.87574e6i | −0.605291 | + | 1.04840i | 0.386714 | + | 0.922200i | \(0.373610\pi\) |
−0.992005 | + | 0.126196i | \(0.959723\pi\) | |||||||
\(318\) | 1.39487e6 | + | 2.41599e6i | 0.773511 | + | 1.33976i | ||||
\(319\) | 64030.8 | + | 110905.i | 0.0352300 | + | 0.0610201i | ||||
\(320\) | 5.93909e6 | − | 1.02868e7i | 3.24224 | − | 5.61572i | ||||
\(321\) | 1.93544e6 | 1.04837 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.04055e6 | −1.08828 | ||||||||
\(324\) | −305654. | + | 529408.i | −0.161759 | + | 0.280174i | ||||
\(325\) | −132012. | − | 228652.i | −0.0693275 | − | 0.120079i | ||||
\(326\) | −3.28373e6 | − | 5.68759e6i | −1.71129 | − | 2.96404i | ||||
\(327\) | 182088. | − | 315385.i | 0.0941697 | − | 0.163107i | ||||
\(328\) | −1.20575e7 | −6.18830 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.08862e6 | −0.550291 | ||||||||
\(331\) | 1.27173e6 | − | 2.20270e6i | 0.638005 | − | 1.10506i | −0.347865 | − | 0.937544i | \(-0.613093\pi\) |
0.985870 | − | 0.167512i | \(-0.0535733\pi\) | |||||||
\(332\) | −2.96874e6 | − | 5.14201e6i | −1.47818 | − | 2.56028i | ||||
\(333\) | −355854. | − | 616357.i | −0.175858 | − | 0.304594i | ||||
\(334\) | 966757. | − | 1.67447e6i | 0.474188 | − | 0.821318i | ||||
\(335\) | −898156. | −0.437260 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.57641e6 | −1.23578 | −0.617888 | − | 0.786266i | \(-0.712012\pi\) | ||||
−0.617888 | + | 0.786266i | \(0.712012\pi\) | |||||||
\(338\) | −1.39861e6 | + | 2.42247e6i | −0.665896 | + | 1.15337i | ||||
\(339\) | 67511.8 | + | 116934.i | 0.0319066 | + | 0.0552638i | ||||
\(340\) | 2.90073e6 | + | 5.02421e6i | 1.36085 | + | 2.35706i | ||||
\(341\) | −213398. | + | 369616.i | −0.0993811 | + | 0.172133i | ||||
\(342\) | 1.85068e6 | 0.855593 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 7.06108e6 | 3.21718 | ||||||||
\(345\) | −546722. | + | 946950.i | −0.247297 | + | 0.428331i | ||||
\(346\) | −28474.0 | − | 49318.4i | −0.0127867 | − | 0.0221472i | ||||
\(347\) | 995177. | + | 1.72370e6i | 0.443687 | + | 0.768488i | 0.997960 | − | 0.0638470i | \(-0.0203369\pi\) |
−0.554273 | + | 0.832335i | \(0.687004\pi\) | |||||||
\(348\) | −309481. | + | 536038.i | −0.136989 | + | 0.237272i | ||||
\(349\) | 1.37419e6 | 0.603926 | 0.301963 | − | 0.953320i | \(-0.402358\pi\) | ||||
0.301963 | + | 0.953320i | \(0.402358\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 253870. | 0.109988 | ||||||||
\(352\) | −2.63804e6 | + | 4.56923e6i | −1.13482 | + | 1.96556i | ||||
\(353\) | 1.46833e6 | + | 2.54323e6i | 0.627174 | + | 1.08630i | 0.988116 | + | 0.153710i | \(0.0491220\pi\) |
−0.360942 | + | 0.932588i | \(0.617545\pi\) | |||||||
\(354\) | −174076. | − | 301509.i | −0.0738297 | − | 0.127877i | ||||
\(355\) | −945243. | + | 1.63721e6i | −0.398082 | + | 0.689498i | ||||
\(356\) | 4.32242e6 | 1.80760 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.71063e6 | −1.11779 | ||||||||
\(359\) | −692873. | + | 1.20009e6i | −0.283738 | + | 0.491449i | −0.972302 | − | 0.233727i | \(-0.924908\pi\) |
0.688564 | + | 0.725175i | \(0.258241\pi\) | |||||||
\(360\) | −1.72728e6 | − | 2.99173e6i | −0.702435 | − | 1.21665i | ||||
\(361\) | −847182. | − | 1.46736e6i | −0.342144 | − | 0.592611i | ||||
\(362\) | −2.75368e6 | + | 4.76952e6i | −1.10444 | + | 1.91295i | ||||
\(363\) | −1.17855e6 | −0.469443 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.35167e6 | −2.10260 | ||||||||
\(366\) | 803346. | − | 1.39144e6i | 0.313473 | − | 0.542951i | ||||
\(367\) | −1.82044e6 | − | 3.15310e6i | −0.705523 | − | 1.22200i | −0.966502 | − | 0.256658i | \(-0.917379\pi\) |
0.260979 | − | 0.965344i | \(-0.415955\pi\) | |||||||
\(368\) | 4.55800e6 | + | 7.89469e6i | 1.75451 | + | 3.03889i | ||||
\(369\) | −713504. | + | 1.23582e6i | −0.272791 | + | 0.472488i | ||||
\(370\) | 6.12583e6 | 2.32627 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2.06284e6 | −0.772873 | ||||||||
\(373\) | −2.07469e6 | + | 3.59347e6i | −0.772114 | + | 1.33734i | 0.164289 | + | 0.986412i | \(0.447467\pi\) |
−0.936402 | + | 0.350928i | \(0.885866\pi\) | |||||||
\(374\) | −969766. | − | 1.67968e6i | −0.358499 | − | 0.620939i | ||||
\(375\) | −663704. | − | 1.14957e6i | −0.243723 | − | 0.422140i | ||||
\(376\) | −25685.2 | + | 44488.1i | −0.00936944 | + | 0.0162283i | ||||
\(377\) | 257049. | 0.0931457 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.26316e6 | −0.451711 | −0.225856 | − | 0.974161i | \(-0.572518\pi\) | ||||
−0.225856 | + | 0.974161i | \(0.572518\pi\) | |||||||
\(380\) | −5.92850e6 | + | 1.02685e7i | −2.10613 | + | 3.64793i | ||||
\(381\) | −532468. | − | 922262.i | −0.187924 | − | 0.325493i | ||||
\(382\) | −1.13967e6 | − | 1.97396e6i | −0.399595 | − | 0.692119i | ||||
\(383\) | 1.14094e6 | − | 1.97617e6i | 0.397435 | − | 0.688377i | −0.595974 | − | 0.803004i | \(-0.703234\pi\) |
0.993409 | + | 0.114627i | \(0.0365672\pi\) | |||||||
\(384\) | −1.04353e7 | −3.61140 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 683148. | 0.233371 | ||||||||
\(387\) | 417842. | − | 723723.i | 0.141819 | − | 0.245638i | ||||
\(388\) | −999801. | − | 1.73171e6i | −0.337159 | − | 0.583976i | ||||
\(389\) | −1.62934e6 | − | 2.82211e6i | −0.545932 | − | 0.945582i | −0.998548 | − | 0.0538762i | \(-0.982842\pi\) |
0.452616 | − | 0.891706i | \(-0.350491\pi\) | |||||||
\(390\) | −1.09256e6 | + | 1.89237e6i | −0.363733 | + | 0.630004i | ||||
\(391\) | −1.94812e6 | −0.644428 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.97519e6 | −0.645100 | ||||||||
\(394\) | 2.56058e6 | − | 4.43505e6i | 0.830993 | − | 1.43932i | ||||
\(395\) | 237210. | + | 410860.i | 0.0764962 | + | 0.132495i | ||||
\(396\) | 654684. | + | 1.13395e6i | 0.209794 | + | 0.363374i | ||||
\(397\) | 2.24742e6 | − | 3.89265e6i | 0.715663 | − | 1.23957i | −0.247040 | − | 0.969005i | \(-0.579458\pi\) |
0.962703 | − | 0.270560i | \(-0.0872089\pi\) | |||||||
\(398\) | 3.02690e6 | 0.957835 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.54490e6 | 1.10778 | ||||||||
\(401\) | −276020. | + | 478080.i | −0.0857194 | + | 0.148470i | −0.905698 | − | 0.423925i | \(-0.860652\pi\) |
0.819978 | + | 0.572395i | \(0.193986\pi\) | |||||||
\(402\) | 725650. | + | 1.25686e6i | 0.223956 | + | 0.387903i | ||||
\(403\) | 428339. | + | 741904.i | 0.131379 | + | 0.227554i | ||||
\(404\) | −6.79850e6 | + | 1.17753e7i | −2.07233 | + | 3.58939i | ||||
\(405\) | −408849. | −0.123858 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.52442e6 | −0.456160 | ||||||||
\(408\) | 3.07739e6 | − | 5.33019e6i | 0.915233 | − | 1.58523i | ||||
\(409\) | −3.02619e6 | − | 5.24152e6i | −0.894517 | − | 1.54935i | −0.834402 | − | 0.551157i | \(-0.814187\pi\) |
−0.0601148 | − | 0.998191i | \(-0.519147\pi\) | |||||||
\(410\) | −6.14128e6 | − | 1.06370e7i | −1.80426 | − | 3.12507i | ||||
\(411\) | 647923. | − | 1.12224e6i | 0.189199 | − | 0.327702i | ||||
\(412\) | 1.54321e7 | 4.47901 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.76686e6 | 0.506641 | ||||||||
\(415\) | 1.98552e6 | − | 3.43903e6i | 0.565920 | − | 0.980202i | ||||
\(416\) | 5.29516e6 | + | 9.17149e6i | 1.50019 | + | 2.59840i | ||||
\(417\) | −1.09937e6 | − | 1.90417e6i | −0.309603 | − | 0.536249i | ||||
\(418\) | 1.98200e6 | − | 3.43293e6i | 0.554834 | − | 0.961001i | ||||
\(419\) | −1.48630e6 | −0.413592 | −0.206796 | − | 0.978384i | \(-0.566304\pi\) | ||||
−0.206796 | + | 0.978384i | \(0.566304\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.40434e6 | −0.386159 | −0.193079 | − | 0.981183i | \(-0.561847\pi\) | ||||
−0.193079 | + | 0.981183i | \(0.561847\pi\) | |||||||
\(422\) | 5.21995e6 | − | 9.04121e6i | 1.42687 | − | 2.47141i | ||||
\(423\) | 3039.86 | + | 5265.19i | 0.000826043 | + | 0.00143075i | ||||
\(424\) | 9.48094e6 | + | 1.64215e7i | 2.56116 | + | 4.43606i | ||||
\(425\) | −378779. | + | 656064.i | −0.101722 | + | 0.176187i | ||||
\(426\) | 3.05477e6 | 0.815557 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2.00367e7 | 5.28709 | ||||||||
\(429\) | 271884. | − | 470916.i | 0.0713247 | − | 0.123538i | ||||
\(430\) | 3.59645e6 | + | 6.22924e6i | 0.938001 | + | 1.62467i | ||||
\(431\) | 1.35087e6 | + | 2.33977e6i | 0.350283 | + | 0.606709i | 0.986299 | − | 0.164968i | \(-0.0527519\pi\) |
−0.636016 | + | 0.771676i | \(0.719419\pi\) | |||||||
\(432\) | −1.70428e6 | + | 2.95190e6i | −0.439371 | + | 0.761013i | ||||
\(433\) | −4.76987e6 | −1.22261 | −0.611304 | − | 0.791396i | \(-0.709355\pi\) | ||||
−0.611304 | + | 0.791396i | \(0.709355\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −413969. | −0.104892 | ||||||||
\(436\) | 1.88507e6 | − | 3.26504e6i | 0.474910 | − | 0.822569i | ||||
\(437\) | −1.99078e6 | − | 3.44813e6i | −0.498678 | − | 0.863735i | ||||
\(438\) | 4.32379e6 | + | 7.48902e6i | 1.07691 | + | 1.86526i | ||||
\(439\) | −3163.74 | + | 5479.77i | −0.000783502 | + | 0.00135707i | −0.866417 | − | 0.499321i | \(-0.833583\pi\) |
0.865633 | + | 0.500678i | \(0.166916\pi\) | |||||||
\(440\) | −7.39935e6 | −1.82206 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.89309e6 | −0.947848 | ||||||||
\(443\) | −707944. | + | 1.22620e6i | −0.171392 | + | 0.296859i | −0.938907 | − | 0.344172i | \(-0.888160\pi\) |
0.767515 | + | 0.641031i | \(0.221493\pi\) | |||||||
\(444\) | −3.68400e6 | − | 6.38087e6i | −0.886874 | − | 1.53611i | ||||
\(445\) | 1.44544e6 | + | 2.50357e6i | 0.346019 | + | 0.599322i | ||||
\(446\) | −1.10223e6 | + | 1.90912e6i | −0.262383 | + | 0.454460i | ||||
\(447\) | −2.51792e6 | −0.596038 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.88150e6 | −0.440442 | −0.220221 | − | 0.975450i | \(-0.570678\pi\) | ||||
−0.220221 | + | 0.975450i | \(0.570678\pi\) | |||||||
\(450\) | 343535. | − | 595019.i | 0.0799722 | − | 0.138516i | ||||
\(451\) | 1.52826e6 | + | 2.64703e6i | 0.353799 | + | 0.612798i | ||||
\(452\) | 698919. | + | 1.21056e6i | 0.160909 | + | 0.278703i | ||||
\(453\) | 901877. | − | 1.56210e6i | 0.206491 | − | 0.357653i | ||||
\(454\) | 1.34076e7 | 3.05290 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.25791e7 | 2.83294 | ||||||||
\(457\) | −3.72211e6 | + | 6.44688e6i | −0.833678 | + | 1.44397i | 0.0614236 | + | 0.998112i | \(0.480436\pi\) |
−0.895102 | + | 0.445861i | \(0.852897\pi\) | |||||||
\(458\) | −1.36533e6 | − | 2.36482e6i | −0.304140 | − | 0.526786i | ||||
\(459\) | −364211. | − | 630831.i | −0.0806902 | − | 0.139760i | ||||
\(460\) | −5.65996e6 | + | 9.80334e6i | −1.24715 | + | 2.16013i | ||||
\(461\) | 7.95698e6 | 1.74380 | 0.871899 | − | 0.489686i | \(-0.162888\pi\) | ||||
0.871899 | + | 0.489686i | \(0.162888\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.64462e6 | 1.44051 | 0.720257 | − | 0.693707i | \(-0.244024\pi\) | ||||
0.720257 | + | 0.693707i | \(0.244024\pi\) | |||||||
\(464\) | −1.72562e6 | + | 2.98886e6i | −0.372092 | + | 0.644483i | ||||
\(465\) | −689824. | − | 1.19481e6i | −0.147947 | − | 0.256252i | ||||
\(466\) | −851750. | − | 1.47527e6i | −0.181697 | − | 0.314708i | ||||
\(467\) | 1.48767e6 | − | 2.57671e6i | 0.315655 | − | 0.546731i | −0.663921 | − | 0.747803i | \(-0.731109\pi\) |
0.979577 | + | 0.201071i | \(0.0644423\pi\) | |||||||
\(468\) | 2.62820e6 | 0.554682 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −52329.5 | −0.0109270 | ||||||||
\(471\) | −2.11501e6 | + | 3.66330e6i | −0.439299 | + | 0.760888i | ||||
\(472\) | −1.18319e6 | − | 2.04935e6i | −0.244456 | − | 0.423410i | ||||
\(473\) | −894980. | − | 1.55015e6i | −0.183933 | − | 0.318582i | ||||
\(474\) | 383299. | − | 663894.i | 0.0783596 | − | 0.135723i | ||||
\(475\) | −1.54829e6 | −0.314861 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.24415e6 | 0.451602 | ||||||||
\(478\) | 8.45112e6 | − | 1.46378e7i | 1.69178 | − | 2.93025i | ||||
\(479\) | 1.70429e6 | + | 2.95192e6i | 0.339395 | + | 0.587849i | 0.984319 | − | 0.176398i | \(-0.0564445\pi\) |
−0.644924 | + | 0.764246i | \(0.723111\pi\) | |||||||
\(480\) | −8.52767e6 | − | 1.47704e7i | −1.68938 | − | 2.92609i | ||||
\(481\) | −1.52993e6 | + | 2.64991e6i | −0.301514 | + | 0.522238i | ||||
\(482\) | −2.60614e6 | −0.510951 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.22010e7 | −2.36747 | ||||||||
\(485\) | 668677. | − | 1.15818e6i | 0.129081 | − | 0.223575i | ||||
\(486\) | 330322. | + | 572135.i | 0.0634377 | + | 0.109877i | ||||
\(487\) | −2.95653e6 | − | 5.12087e6i | −0.564886 | − | 0.978410i | −0.997060 | − | 0.0766206i | \(-0.975587\pi\) |
0.432175 | − | 0.901790i | \(-0.357746\pi\) | |||||||
\(488\) | 5.46034e6 | − | 9.45758e6i | 1.03793 | − | 1.79776i | ||||
\(489\) | −5.28305e6 | −0.999108 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 549890. | 0.102937 | 0.0514686 | − | 0.998675i | \(-0.483610\pi\) | ||||
0.0514686 | + | 0.998675i | \(0.483610\pi\) | |||||||
\(492\) | −7.38658e6 | + | 1.27939e7i | −1.37572 | + | 2.38282i | ||||
\(493\) | −368772. | − | 638731.i | −0.0683345 | − | 0.118359i | ||||
\(494\) | −3.97834e6 | − | 6.89068e6i | −0.733473 | − | 1.27041i | ||||
\(495\) | −437859. | + | 758394.i | −0.0803195 | + | 0.139118i | ||||
\(496\) | −1.15021e7 | −2.09929 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −6.41668e6 | −1.15941 | ||||||||
\(499\) | −2.80472e6 | + | 4.85792e6i | −0.504241 | + | 0.873372i | 0.495746 | + | 0.868467i | \(0.334895\pi\) |
−0.999988 | + | 0.00490459i | \(0.998439\pi\) | |||||||
\(500\) | −6.87102e6 | − | 1.19010e7i | −1.22913 | − | 2.12891i | ||||
\(501\) | −777686. | − | 1.34699e6i | −0.138424 | − | 0.239757i | ||||
\(502\) | 4.26672e6 | − | 7.39018e6i | 0.755675 | − | 1.30887i | ||||
\(503\) | 1.43167e6 | 0.252304 | 0.126152 | − | 0.992011i | \(-0.459737\pi\) | ||||
0.126152 | + | 0.992011i | \(0.459737\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.09381e6 | −1.58678 | ||||||||
\(506\) | 1.89223e6 | − | 3.27743e6i | 0.328546 | − | 0.569059i | ||||
\(507\) | 1.12509e6 | + | 1.94870e6i | 0.194386 | + | 0.336687i | ||||
\(508\) | −5.51240e6 | − | 9.54776e6i | −0.947724 | − | 1.64151i | ||||
\(509\) | 2.69919e6 | − | 4.67513e6i | 0.461784 | − | 0.799833i | −0.537266 | − | 0.843413i | \(-0.680543\pi\) |
0.999050 | + | 0.0435796i | \(0.0138762\pi\) | |||||||
\(510\) | 6.26968e6 | 1.06738 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −3.97880e7 | −6.70775 | ||||||||
\(513\) | 744371. | − | 1.28929e6i | 0.124881 | − | 0.216300i | ||||
\(514\) | 7.72602e6 | + | 1.33819e7i | 1.28988 | + | 2.23413i | ||||
\(515\) | 5.16057e6 | + | 8.93837e6i | 0.857392 | + | 1.48505i | ||||
\(516\) | 4.32573e6 | − | 7.49238e6i | 0.715212 | − | 1.23878i | ||||
\(517\) | 13022.2 | 0.00214269 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −45810.6 | −0.00746530 | ||||||||
\(520\) | −7.42611e6 | + | 1.28624e7i | −1.20435 | + | 2.08600i | ||||
\(521\) | 784443. | + | 1.35870e6i | 0.126610 | + | 0.219295i | 0.922361 | − | 0.386329i | \(-0.126257\pi\) |
−0.795751 | + | 0.605624i | \(0.792924\pi\) | |||||||
\(522\) | 334459. | + | 579300.i | 0.0537237 | + | 0.0930523i | ||||
\(523\) | −2.31659e6 | + | 4.01246e6i | −0.370336 | + | 0.641440i | −0.989617 | − | 0.143729i | \(-0.954091\pi\) |
0.619281 | + | 0.785169i | \(0.287424\pi\) | |||||||
\(524\) | −2.04482e7 | −3.25333 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.08888e6 | 1.11715 | ||||||||
\(527\) | 1.22902e6 | − | 2.12872e6i | 0.192767 | − | 0.333882i | ||||
\(528\) | 3.65042e6 | + | 6.32271e6i | 0.569846 | + | 0.987002i | ||||
\(529\) | 1.31756e6 | + | 2.28209e6i | 0.204707 | + | 0.354563i | ||||
\(530\) | −9.65794e6 | + | 1.67280e7i | −1.49346 | + | 2.58676i | ||||
\(531\) | −280063. | −0.0431042 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.13515e6 | 0.935421 | ||||||||
\(534\) | 2.33563e6 | − | 4.04544e6i | 0.354447 | − | 0.613920i | ||||
\(535\) | 6.70037e6 | + | 1.16054e7i | 1.01208 | + | 1.75297i | ||||
\(536\) | 4.93224e6 | + | 8.54289e6i | 0.741536 | + | 1.28438i | ||||
\(537\) | −1.09025e6 | + | 1.88837e6i | −0.163152 | + | 0.282587i | ||||
\(538\) | 229733. | 0.0342190 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −4.23263e6 | −0.624634 | ||||||||
\(541\) | −5.18789e6 | + | 8.98568e6i | −0.762074 | + | 1.31995i | 0.179705 | + | 0.983720i | \(0.442486\pi\) |
−0.941780 | + | 0.336231i | \(0.890848\pi\) | |||||||
\(542\) | −1.23594e7 | − | 2.14071e7i | −1.80717 | − | 3.13011i | ||||
\(543\) | 2.21514e6 | + | 3.83674e6i | 0.322405 | + | 0.558422i | ||||
\(544\) | 1.51932e7 | − | 2.63155e7i | 2.20117 | − | 3.81253i | ||||
\(545\) | 2.52151e6 | 0.363638 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.07555e7 | 1.53695 | 0.768476 | − | 0.639879i | \(-0.221015\pi\) | ||||
0.768476 | + | 0.639879i | \(0.221015\pi\) | |||||||
\(548\) | 6.70766e6 | − | 1.16180e7i | 0.954156 | − | 1.65265i | ||||
\(549\) | −646234. | − | 1.11931e6i | −0.0915080 | − | 0.158497i | ||||
\(550\) | −735821. | − | 1.27448e6i | −0.103721 | − | 0.179649i | ||||
\(551\) | 753693. | − | 1.30543e6i | 0.105759 | − | 0.183179i | ||||
\(552\) | 1.20093e7 | 1.67753 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 7.60610e6 | 1.05290 | ||||||||
\(555\) | 2.46389e6 | − | 4.26759e6i | 0.339539 | − | 0.588099i | ||||
\(556\) | −1.13813e7 | − | 1.97130e7i | −1.56137 | − | 2.70437i | ||||
\(557\) | 1.68656e6 | + | 2.92120e6i | 0.230337 | + | 0.398955i | 0.957907 | − | 0.287078i | \(-0.0926839\pi\) |
−0.727570 | + | 0.686033i | \(0.759351\pi\) | |||||||
\(558\) | −1.11466e6 | + | 1.93065e6i | −0.151551 | + | 0.262494i | ||||
\(559\) | −3.59286e6 | −0.486308 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.56021e6 | −0.209304 | ||||||||
\(562\) | −4.65342e6 | + | 8.05997e6i | −0.621487 | + | 1.07645i | ||||
\(563\) | 4.88201e6 | + | 8.45589e6i | 0.649124 | + | 1.12432i | 0.983332 | + | 0.181817i | \(0.0581977\pi\) |
−0.334209 | + | 0.942499i | \(0.608469\pi\) | |||||||
\(564\) | 31470.3 | + | 54508.1i | 0.00416584 | + | 0.00721545i | ||||
\(565\) | −467444. | + | 809637.i | −0.0616039 | + | 0.106701i | ||||
\(566\) | −2.58524e7 | −3.39203 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.07633e7 | 2.70038 | ||||||||
\(569\) | 4.51973e6 | − | 7.82839e6i | 0.585236 | − | 1.01366i | −0.409609 | − | 0.912261i | \(-0.634335\pi\) |
0.994846 | − | 0.101398i | \(-0.0323317\pi\) | |||||||
\(570\) | 6.40697e6 | + | 1.10972e7i | 0.825972 | + | 1.43063i | ||||
\(571\) | 5.34963e6 | + | 9.26582e6i | 0.686646 | + | 1.18931i | 0.972916 | + | 0.231158i | \(0.0742513\pi\) |
−0.286270 | + | 0.958149i | \(0.592415\pi\) | |||||||
\(572\) | 2.81469e6 | − | 4.87518e6i | 0.359700 | − | 0.623019i | ||||
\(573\) | −1.83356e6 | −0.233297 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.47816e6 | −0.186445 | ||||||||
\(576\) | −7.71991e6 | + | 1.33713e7i | −0.969518 | + | 1.67925i | ||||
\(577\) | 2.50031e6 | + | 4.33067e6i | 0.312648 | + | 0.541521i | 0.978935 | − | 0.204174i | \(-0.0654508\pi\) |
−0.666287 | + | 0.745695i | \(0.732117\pi\) | |||||||
\(578\) | −2.35757e6 | − | 4.08344e6i | −0.293525 | − | 0.508401i | ||||
\(579\) | 274772. | − | 475919.i | 0.0340624 | − | 0.0589979i | ||||
\(580\) | −4.28563e6 | −0.528987 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −2.16098e6 | −0.264450 | ||||||||
\(583\) | 2.40338e6 | − | 4.16278e6i | 0.292854 | − | 0.507239i | ||||
\(584\) | 2.93888e7 | + | 5.09028e7i | 3.56574 | + | 6.17604i | ||||
\(585\) | 878884. | + | 1.52227e6i | 0.106180 | + | 0.183909i | ||||
\(586\) | 8.65780e6 | − | 1.49958e7i | 1.04151 | − | 1.80395i | ||||
\(587\) | −7.54203e6 | −0.903427 | −0.451713 | − | 0.892163i | \(-0.649187\pi\) | ||||
−0.451713 | + | 0.892163i | \(0.649187\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.02372e6 | 0.596674 | ||||||||
\(590\) | 1.20528e6 | − | 2.08761e6i | 0.142547 | − | 0.246899i | ||||
\(591\) | −2.05980e6 | − | 3.56768e6i | −0.242581 | − | 0.420162i | ||||
\(592\) | −2.05414e7 | − | 3.55788e7i | −2.40894 | − | 4.17240i | ||||
\(593\) | 2.99832e6 | − | 5.19324e6i | 0.350139 | − | 0.606459i | −0.636134 | − | 0.771578i | \(-0.719468\pi\) |
0.986274 | + | 0.165119i | \(0.0528009\pi\) | |||||||
\(594\) | 1.41504e6 | 0.164552 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.60669e7 | −3.00590 | ||||||||
\(597\) | 1.21746e6 | − | 2.10871e6i | 0.139804 | − | 0.242148i | ||||
\(598\) | −3.79814e6 | − | 6.57856e6i | −0.434328 | − | 0.752278i | ||||
\(599\) | 3.77075e6 | + | 6.53113e6i | 0.429399 | + | 0.743740i | 0.996820 | − | 0.0796875i | \(-0.0253922\pi\) |
−0.567421 | + | 0.823428i | \(0.692059\pi\) | |||||||
\(600\) | 2.33500e6 | − | 4.04434e6i | 0.264795 | − | 0.458638i | ||||
\(601\) | −2.34440e6 | −0.264756 | −0.132378 | − | 0.991199i | \(-0.542261\pi\) | ||||
−0.132378 | + | 0.991199i | \(0.542261\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.16747e6 | 0.130753 | ||||||||
\(604\) | 9.33672e6 | − | 1.61717e7i | 1.04136 | − | 1.80369i | ||||
\(605\) | −4.08009e6 | − | 7.06692e6i | −0.453191 | − | 0.784950i | ||||
\(606\) | 7.34718e6 | + | 1.27257e7i | 0.812717 | + | 1.40767i | ||||
\(607\) | −7.09702e6 | + | 1.22924e7i | −0.781816 | + | 1.35414i | 0.149067 | + | 0.988827i | \(0.452373\pi\) |
−0.930883 | + | 0.365318i | \(0.880960\pi\) | |||||||
\(608\) | 6.21037e7 | 6.81332 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.11246e7 | 1.21048 | ||||||||
\(611\) | 13069.3 | − | 22636.7i | 0.00141628 | − | 0.00245307i | ||||
\(612\) | −3.77051e6 | − | 6.53071e6i | −0.406932 | − | 0.704826i | ||||
\(613\) | −7.68994e6 | − | 1.33194e7i | −0.826555 | − | 1.43164i | −0.900725 | − | 0.434390i | \(-0.856964\pi\) |
0.0741701 | − | 0.997246i | \(-0.476369\pi\) | |||||||
\(614\) | 837229. | − | 1.45012e6i | 0.0896238 | − | 0.155233i | ||||
\(615\) | −9.88044e6 | −1.05339 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.26335e6 | −0.345105 | −0.172552 | − | 0.985000i | \(-0.555201\pi\) | ||||
−0.172552 | + | 0.985000i | \(0.555201\pi\) | |||||||
\(618\) | 8.33879e6 | − | 1.44432e7i | 0.878277 | − | 1.52122i | ||||
\(619\) | 5.73811e6 | + | 9.93869e6i | 0.601924 | + | 1.04256i | 0.992529 | + | 0.122005i | \(0.0389325\pi\) |
−0.390605 | + | 0.920558i | \(0.627734\pi\) | |||||||
\(620\) | −7.14144e6 | − | 1.23693e7i | −0.746116 | − | 1.29231i | ||||
\(621\) | 710655. | − | 1.23089e6i | 0.0739486 | − | 0.128083i | ||||
\(622\) | 1.63891e6 | 0.169855 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.46545e7 | 1.50664 | ||||||||
\(625\) | 5.78003e6 | − | 1.00113e7i | 0.591875 | − | 1.02516i | ||||
\(626\) | 1.78078e6 | + | 3.08440e6i | 0.181624 | + | 0.314582i | ||||
\(627\) | −1.59438e6 | − | 2.76154e6i | −0.161965 | − | 0.280532i | ||||
\(628\) | −2.18957e7 | + | 3.79245e7i | −2.21544 | + | 3.83726i | ||||
\(629\) | 8.77954e6 | 0.884800 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.11249e6 | 0.911095 | 0.455548 | − | 0.890211i | \(-0.349444\pi\) | ||||
0.455548 | + | 0.890211i | \(0.349444\pi\) | |||||||
\(632\) | 2.60528e6 | − | 4.51248e6i | 0.259455 | − | 0.449389i | ||||
\(633\) | −4.19907e6 | − | 7.27300e6i | −0.416528 | − | 0.721447i | ||||
\(634\) | 1.21162e7 | + | 2.09859e7i | 1.19714 | + | 2.07351i | ||||
\(635\) | 3.68675e6 | − | 6.38564e6i | 0.362835 | − | 0.628449i | ||||
\(636\) | 2.32327e7 | 2.27749 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.43276e6 | 0.139355 | ||||||||
\(639\) | 1.22867e6 | − | 2.12812e6i | 0.119037 | − | 0.206179i | ||||
\(640\) | −3.61263e7 | − | 6.25726e7i | −3.48637 | − | 6.03857i | ||||
\(641\) | 6.70607e6 | + | 1.16153e7i | 0.644649 | + | 1.11656i | 0.984383 | + | 0.176043i | \(0.0563297\pi\) |
−0.339734 | + | 0.940522i | \(0.610337\pi\) | |||||||
\(642\) | 1.08269e7 | − | 1.87527e7i | 1.03673 | − | 1.79567i | ||||
\(643\) | 5.00517e6 | 0.477410 | 0.238705 | − | 0.971092i | \(-0.423277\pi\) | ||||
0.238705 | + | 0.971092i | \(0.423277\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.78618e6 | 0.547637 | ||||||||
\(646\) | −1.14149e7 | + | 1.97712e7i | −1.07620 | + | 1.86403i | ||||
\(647\) | 2.91762e6 | + | 5.05346e6i | 0.274011 | + | 0.474601i | 0.969885 | − | 0.243563i | \(-0.0783162\pi\) |
−0.695874 | + | 0.718164i | \(0.744983\pi\) | |||||||
\(648\) | 2.24520e6 | + | 3.88880e6i | 0.210047 | + | 0.363813i | ||||
\(649\) | −299936. | + | 519504.i | −0.0279522 | + | 0.0484147i | ||||
\(650\) | −2.95392e6 | −0.274231 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.46930e7 | −5.03864 | ||||||||
\(653\) | −7.56843e6 | + | 1.31089e7i | −0.694581 | + | 1.20305i | 0.275741 | + | 0.961232i | \(0.411077\pi\) |
−0.970322 | + | 0.241817i | \(0.922257\pi\) | |||||||
\(654\) | −2.03721e6 | − | 3.52855e6i | −0.186248 | − | 0.322591i | ||||
\(655\) | −6.83799e6 | − | 1.18437e7i | −0.622766 | − | 1.07866i | ||||
\(656\) | −4.11865e7 | + | 7.13371e7i | −3.73676 | + | 6.47225i | ||||
\(657\) | 6.95635e6 | 0.628736 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.26786e7 | 1.13725 | 0.568625 | − | 0.822597i | \(-0.307475\pi\) | ||||
0.568625 | + | 0.822597i | \(0.307475\pi\) | |||||||
\(660\) | −4.53296e6 | + | 7.85131e6i | −0.405062 | + | 0.701588i | ||||
\(661\) | −700122. | − | 1.21265e6i | −0.0623261 | − | 0.107952i | 0.833179 | − | 0.553004i | \(-0.186519\pi\) |
−0.895505 | + | 0.445052i | \(0.853185\pi\) | |||||||
\(662\) | −1.42282e7 | − | 2.46439e7i | −1.26184 | − | 2.18557i | ||||
\(663\) | −1.56586e6 | + | 2.71214e6i | −0.138346 | + | 0.239623i | ||||
\(664\) | −4.36141e7 | −3.83890 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.96264e6 | −0.695619 | ||||||||
\(667\) | 719554. | − | 1.24630e6i | 0.0626252 | − | 0.108470i | ||||
\(668\) | −8.05103e6 | − | 1.39448e7i | −0.698089 | − | 1.20912i | ||||
\(669\) | 886664. | + | 1.53575e6i | 0.0765939 | + | 0.132664i | ||||
\(670\) | −5.02432e6 | + | 8.70238e6i | −0.432405 | + | 0.748947i | ||||
\(671\) | −2.76835e6 | −0.237364 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.01514e6 | −0.511927 | −0.255963 | − | 0.966686i | \(-0.582393\pi\) | ||||
−0.255963 | + | 0.966686i | \(0.582393\pi\) | |||||||
\(674\) | −1.44125e7 | + | 2.49632e7i | −1.22205 | + | 2.11666i | ||||
\(675\) | −276349. | − | 478650.i | −0.0233452 | − | 0.0404351i | ||||
\(676\) | 1.16475e7 | + | 2.01741e7i | 0.980316 | + | 1.69796i | ||||
\(677\) | 3.30005e6 | − | 5.71585e6i | 0.276725 | − | 0.479302i | −0.693844 | − | 0.720125i | \(-0.744084\pi\) |
0.970569 | + | 0.240824i | \(0.0774176\pi\) | |||||||
\(678\) | 1.51065e6 | 0.126209 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4.26150e7 | 3.53419 | ||||||||
\(681\) | 5.39273e6 | − | 9.34049e6i | 0.445596 | − | 0.771795i | ||||
\(682\) | 2.38751e6 | + | 4.13529e6i | 0.196555 | + | 0.340443i | ||||
\(683\) | −106867. | − | 185099.i | −0.00876581 | − | 0.0151828i | 0.861609 | − | 0.507572i | \(-0.169457\pi\) |
−0.870375 | + | 0.492389i | \(0.836124\pi\) | |||||||
\(684\) | 7.70614e6 | − | 1.33474e7i | 0.629791 | − | 1.09083i | ||||
\(685\) | 8.97230e6 | 0.730596 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.19662e6 | −0.177567 | ||||||||
\(688\) | 2.41196e7 | − | 4.17764e7i | 1.94267 | − | 3.36480i | ||||
\(689\) | −4.82415e6 | − | 8.35567e6i | −0.387144 | − | 0.670553i | ||||
\(690\) | 6.11676e6 | + | 1.05945e7i | 0.489101 | + | 0.847148i | ||||
\(691\) | 717549. | − | 1.24283e6i | 0.0571684 | − | 0.0990187i | −0.836025 | − | 0.548692i | \(-0.815126\pi\) |
0.893193 | + | 0.449673i | \(0.148459\pi\) | |||||||
\(692\) | −474256. | −0.0376485 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.22682e7 | 1.75504 | ||||||||
\(695\) | 7.61195e6 | − | 1.31843e7i | 0.597770 | − | 1.03537i | ||||
\(696\) | 2.27331e6 | + | 3.93750e6i | 0.177884 | + | 0.308104i | ||||
\(697\) | −8.80170e6 | − | 1.52450e7i | −0.686253 | − | 1.18863i | ||||
\(698\) | 7.68727e6 | − | 1.33147e7i | 0.597219 | − | 1.03441i | ||||
\(699\) | −1.37034e6 | −0.106081 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.27397e7 | −0.979186 | −0.489593 | − | 0.871951i | \(-0.662855\pi\) | ||||
−0.489593 | + | 0.871951i | \(0.662855\pi\) | |||||||
\(702\) | 1.42016e6 | − | 2.45979e6i | 0.108766 | − | 0.188389i | ||||
\(703\) | 8.97179e6 | + | 1.55396e7i | 0.684685 | + | 1.18591i | ||||
\(704\) | 1.65354e7 | + | 2.86401e7i | 1.25743 | + | 2.17792i | ||||
\(705\) | −21047.6 | + | 36455.6i | −0.00159489 | + | 0.00276243i | ||||
\(706\) | 3.28557e7 | 2.48084 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.89937e6 | −0.217380 | ||||||||
\(709\) | −3.89752e6 | + | 6.75070e6i | −0.291187 | + | 0.504352i | −0.974091 | − | 0.226157i | \(-0.927384\pi\) |
0.682903 | + | 0.730509i | \(0.260717\pi\) | |||||||
\(710\) | 1.05754e7 | + | 1.83172e7i | 0.787323 | + | 1.36368i | ||||
\(711\) | −308337. | − | 534055.i | −0.0228745 | − | 0.0396198i | ||||
\(712\) | 1.58753e7 | − | 2.74968e7i | 1.17360 | − | 2.03274i | ||||
\(713\) | 4.79617e6 | 0.353322 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.76498e6 | 0.275422 | ||||||||
\(716\) | −1.12869e7 | + | 1.95495e7i | −0.822795 | + | 1.42512i | ||||
\(717\) | −6.79832e6 | − | 1.17750e7i | −0.493860 | − | 0.855390i | ||||
\(718\) | 7.75191e6 | + | 1.34267e7i | 0.561174 | + | 0.971982i | ||||
\(719\) | −2.43480e6 | + | 4.21720e6i | −0.175647 | + | 0.304230i | −0.940385 | − | 0.340112i | \(-0.889535\pi\) |
0.764738 | + | 0.644341i | \(0.222868\pi\) | |||||||
\(720\) | −2.36005e7 | −1.69664 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.89567e7 | −1.35338 | ||||||||
\(723\) | −1.04823e6 | + | 1.81558e6i | −0.0745777 | + | 0.129172i | ||||
\(724\) | 2.29324e7 | + | 3.97200e7i | 1.62593 | + | 2.81620i | ||||
\(725\) | −279810. | − | 484644.i | −0.0197705 | − | 0.0342435i | ||||
\(726\) | −6.59288e6 | + | 1.14192e7i | −0.464230 | + | 0.804070i | ||||
\(727\) | −1.29961e7 | −0.911966 | −0.455983 | − | 0.889989i | \(-0.650712\pi\) | ||||
−0.455983 | + | 0.889989i | \(0.650712\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −2.99374e7 | + | 5.18531e7i | −2.07925 | + | 3.60137i | ||||
\(731\) | 5.15444e6 | + | 8.92776e6i | 0.356770 | + | 0.617944i | ||||
\(732\) | −6.69017e6 | − | 1.15877e7i | −0.461487 | − | 0.799319i | ||||
\(733\) | 2.40302e6 | − | 4.16215e6i | 0.165195 | − | 0.286127i | −0.771529 | − | 0.636194i | \(-0.780508\pi\) |
0.936725 | + | 0.350067i | \(0.113841\pi\) | |||||||
\(734\) | −4.07344e7 | −2.79075 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.92907e7 | 4.03452 | ||||||||
\(737\) | 1.25031e6 | − | 2.16559e6i | 0.0847905 | − | 0.146862i | ||||
\(738\) | 7.98273e6 | + | 1.38265e7i | 0.539524 | + | 0.934483i | ||||
\(739\) | −9.28626e6 | − | 1.60843e7i | −0.625503 | − | 1.08340i | −0.988443 | − | 0.151591i | \(-0.951560\pi\) |
0.362940 | − | 0.931813i | \(-0.381773\pi\) | |||||||
\(740\) | 2.55076e7 | − | 4.41804e7i | 1.71234 | − | 2.96586i | ||||
\(741\) | −6.40057e6 | −0.428226 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.17402e7 | 0.780192 | 0.390096 | − | 0.920774i | \(-0.372442\pi\) | ||||
0.390096 | + | 0.920774i | \(0.372442\pi\) | |||||||
\(744\) | −7.57636e6 | + | 1.31226e7i | −0.501797 | + | 0.869138i | ||||
\(745\) | −8.71691e6 | − | 1.50981e7i | −0.575403 | − | 0.996627i | ||||
\(746\) | 2.32118e7 | + | 4.02040e7i | 1.52708 | + | 2.64498i | ||||
\(747\) | −2.58088e6 | + | 4.47021e6i | −0.169226 | + | 0.293107i | ||||
\(748\) | −1.61522e7 | −1.05555 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.48511e7 | −0.964065 | ||||||||
\(751\) | −7.52507e6 | + | 1.30338e7i | −0.486867 | + | 0.843279i | −0.999886 | − | 0.0150987i | \(-0.995194\pi\) |
0.513019 | + | 0.858377i | \(0.328527\pi\) | |||||||
\(752\) | 175474. | + | 303929.i | 0.0113153 | + | 0.0195987i | ||||
\(753\) | −3.43227e6 | − | 5.94487e6i | −0.220594 | − | 0.382081i | ||||
\(754\) | 1.43794e6 | − | 2.49059e6i | 0.0921114 | − | 0.159542i | ||||
\(755\) | 1.24890e7 | 0.797370 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.04785e6 | 0.129885 | 0.0649423 | − | 0.997889i | \(-0.479314\pi\) | ||||
0.0649423 | + | 0.997889i | \(0.479314\pi\) | |||||||
\(758\) | −7.06617e6 | + | 1.22390e7i | −0.446695 | + | 0.773699i | ||||
\(759\) | −1.52216e6 | − | 2.63646e6i | −0.0959082 | − | 0.166118i | ||||
\(760\) | 4.35481e7 | + | 7.54276e7i | 2.73486 | + | 4.73692i | ||||
\(761\) | −8.25757e6 | + | 1.43025e7i | −0.516881 | + | 0.895264i | 0.482927 | + | 0.875661i | \(0.339574\pi\) |
−0.999808 | + | 0.0196033i | \(0.993760\pi\) | |||||||
\(762\) | −1.19146e7 | −0.743347 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −1.89821e7 | −1.17655 | ||||||||
\(765\) | 2.52175e6 | − | 4.36781e6i | 0.155793 | − | 0.269842i | ||||
\(766\) | −1.27649e7 | − | 2.21095e7i | −0.786042 | − | 1.36147i | ||||
\(767\) | 602040. | + | 1.04276e6i | 0.0369519 | + | 0.0640026i | ||||
\(768\) | −3.09267e7 | + | 5.35666e7i | −1.89204 | + | 3.27711i | ||||
\(769\) | 2.10148e7 | 1.28147 | 0.640736 | − | 0.767761i | \(-0.278629\pi\) | ||||
0.640736 | + | 0.767761i | \(0.278629\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.24301e7 | 0.753073 | ||||||||
\(772\) | 2.84459e6 | − | 4.92697e6i | 0.171781 | − | 0.297534i | ||||
\(773\) | −1.39826e7 | − | 2.42186e7i | −0.841667 | − | 1.45781i | −0.888484 | − | 0.458907i | \(-0.848241\pi\) |
0.0468169 | − | 0.998903i | \(-0.485092\pi\) | |||||||
\(774\) | −4.67484e6 | − | 8.09706e6i | −0.280488 | − | 0.485820i | ||||
\(775\) | 932532. | − | 1.61519e6i | 0.0557711 | − | 0.0965984i | ||||
\(776\) | −1.46882e7 | −0.875616 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.64584e7 | −2.15948 | ||||||||
\(779\) | 1.79889e7 | − | 3.11576e7i | 1.06209 | − | 1.83959i | ||||
\(780\) | 9.09869e6 | + | 1.57594e7i | 0.535479 | + | 0.927477i | ||||
\(781\) | −2.63171e6 | − | 4.55825e6i | −0.154387 | − | 0.267406i | ||||
\(782\) | −1.08979e7 | + | 1.88757e7i | −0.637272 | + | 1.10379i | ||||
\(783\) | 538096. | 0.0313657 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.92882e7 | −1.69636 | ||||||||
\(786\) | −1.10493e7 | + | 1.91379e7i | −0.637936 | + | 1.10494i | ||||
\(787\) | 1.33642e6 | + | 2.31475e6i | 0.0769141 | + | 0.133219i | 0.901917 | − | 0.431909i | \(-0.142160\pi\) |
−0.825003 | + | 0.565128i | \(0.808827\pi\) | |||||||
\(788\) | −2.13242e7 | − | 3.69346e7i | −1.22337 | − | 2.11893i | ||||
\(789\) | 2.85125e6 | − | 4.93850e6i | 0.163058 | − | 0.282425i | ||||
\(790\) | 5.30784e6 | 0.302587 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 9.61803e6 | 0.544845 | ||||||||
\(793\) | −2.77836e6 | + | 4.81227e6i | −0.156894 | + | 0.271748i | ||||
\(794\) | −2.51443e7 | − | 4.35513e7i | −1.41543 | − | 2.45160i | ||||
\(795\) | 7.76912e6 | + | 1.34565e7i | 0.435967 | + | 0.755117i | ||||
\(796\) | 1.26038e7 | − | 2.18305e7i | 0.705051 | − | 1.22118i | ||||
\(797\) | 8.17692e6 | 0.455978 | 0.227989 | − | 0.973664i | \(-0.426785\pi\) | ||||
0.227989 | + | 0.973664i | \(0.426785\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −74998.7 | −0.00415611 | ||||||||
\(800\) | 1.15280e7 | − | 1.99672e7i | 0.636840 | − | 1.10304i | ||||
\(801\) | −1.87885e6 | − | 3.25426e6i | −0.103469 | − | 0.179214i | ||||
\(802\) | 3.08813e6 | + | 5.34879e6i | 0.169535 | + | 0.293643i | ||||
\(803\) | 7.44995e6 | − | 1.29037e7i | 0.407722 | − | 0.706196i | ||||
\(804\) | 1.20863e7 | 0.659404 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9.58457e6 | 0.519679 | ||||||||
\(807\) | 92401.7 | − | 160045.i | 0.00499455 | − | 0.00865081i | ||||
\(808\) | 4.99388e7 | + | 8.64965e7i | 2.69097 | + | 4.66090i | ||||
\(809\) | −1.18901e7 | − | 2.05942e7i | −0.638723 | − | 1.10630i | −0.985713 | − | 0.168432i | \(-0.946130\pi\) |
0.346990 | − | 0.937869i | \(-0.387204\pi\) | |||||||
\(810\) | −2.28711e6 | + | 3.96140e6i | −0.122483 | + | 0.212147i | ||||
\(811\) | 2.42489e7 | 1.29461 | 0.647306 | − | 0.762231i | \(-0.275896\pi\) | ||||
0.647306 | + | 0.762231i | \(0.275896\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.98845e7 | −1.05509 | ||||||||
\(814\) | −8.52764e6 | + | 1.47703e7i | −0.451095 | + | 0.781319i | ||||
\(815\) | −1.82896e7 | − | 3.16786e7i | −0.964519 | − | 1.67060i | ||||
\(816\) | −2.10238e7 | − | 3.64143e7i | −1.10531 | − | 1.91446i | ||||
\(817\) | −1.05346e7 | + | 1.82465e7i | −0.552159 | + | 0.956367i | ||||
\(818\) | −6.77145e7 | −3.53833 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.02288e8 | −5.31238 | ||||||||
\(821\) | 1.80055e6 | − | 3.11864e6i | 0.0932280 | − | 0.161476i | −0.815640 | − | 0.578560i | \(-0.803615\pi\) |
0.908868 | + | 0.417085i | \(0.136948\pi\) | |||||||
\(822\) | −7.24901e6 | − | 1.25557e7i | −0.374196 | − | 0.648127i | ||||
\(823\) | 8.42191e6 | + | 1.45872e7i | 0.433422 | + | 0.750709i | 0.997165 | − | 0.0752410i | \(-0.0239726\pi\) |
−0.563743 | + | 0.825950i | \(0.690639\pi\) | |||||||
\(824\) | 5.66787e7 | − | 9.81704e7i | 2.90805 | − | 5.03689i | ||||
\(825\) | −1.18383e6 | −0.0605556 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.81504e7 | −0.922829 | −0.461415 | − | 0.887185i | \(-0.652658\pi\) | ||||
−0.461415 | + | 0.887185i | \(0.652658\pi\) | |||||||
\(828\) | 7.35709e6 | − | 1.27429e7i | 0.372932 | − | 0.645938i | ||||
\(829\) | −5.36205e6 | − | 9.28735e6i | −0.270985 | − | 0.469359i | 0.698130 | − | 0.715971i | \(-0.254016\pi\) |
−0.969114 | + | 0.246612i | \(0.920683\pi\) | |||||||
\(830\) | −2.22142e7 | − | 3.84761e7i | −1.11927 | − | 1.93863i | ||||
\(831\) | 3.05928e6 | − | 5.29883e6i | 0.153680 | − | 0.266181i | ||||
\(832\) | 6.63806e7 | 3.32455 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −2.45998e7 | −1.22466 | ||||||||
\(835\) | 5.38461e6 | − | 9.32642e6i | 0.267263 | − | 0.462912i | ||||
\(836\) | −1.65059e7 | − | 2.85890e7i | −0.816814 | − | 1.41476i | ||||
\(837\) | 896666. | + | 1.55307e6i | 0.0442402 | + | 0.0766263i | ||||
\(838\) | −8.31442e6 | + | 1.44010e7i | −0.408999 | + | 0.708406i | ||||
\(839\) | 1.18159e7 | 0.579510 | 0.289755 | − | 0.957101i | \(-0.406426\pi\) | ||||
0.289755 | + | 0.957101i | \(0.406426\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.99663e7 | −0.973437 | ||||||||
\(842\) | −7.85591e6 | + | 1.36068e7i | −0.381870 | + | 0.661419i | ||||
\(843\) | 3.74335e6 | + | 6.48367e6i | 0.181422 | + | 0.314233i | ||||
\(844\) | −4.34711e7 | − | 7.52941e7i | −2.10061 | − | 3.63836i | ||||
\(845\) | −7.78996e6 | + | 1.34926e7i | −0.375313 | + | 0.650061i | ||||
\(846\) | 68020.3 | 0.00326748 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.29542e8 | 6.18615 | ||||||||
\(849\) | −1.03982e7 | + | 1.80102e7i | −0.495096 | + | 0.857531i | ||||
\(850\) | 4.23780e6 | + | 7.34009e6i | 0.201184 | + | 0.348461i | ||||
\(851\) | 8.56541e6 | + | 1.48357e7i | 0.405438 | + | 0.702239i | ||||
\(852\) | 1.27199e7 | − | 2.20315e7i | 0.600322 | − | 1.03979i | ||||
\(853\) | 6.26477e6 | 0.294803 | 0.147402 | − | 0.989077i | \(-0.452909\pi\) | ||||
0.147402 | + | 0.989077i | \(0.452909\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.03079e7 | 0.482230 | ||||||||
\(856\) | 7.35903e7 | − | 1.27462e8i | 3.43270 | − | 5.94562i | ||||
\(857\) | 1.25568e7 | + | 2.17491e7i | 0.584020 | + | 1.01155i | 0.994997 | + | 0.0999068i | \(0.0318545\pi\) |
−0.410977 | + | 0.911646i | \(0.634812\pi\) | |||||||
\(858\) | −3.04185e6 | − | 5.26865e6i | −0.141065 | − | 0.244332i | ||||
\(859\) | −2.07327e6 | + | 3.59101e6i | −0.0958679 | + | 0.166048i | −0.909970 | − | 0.414673i | \(-0.863896\pi\) |
0.814103 | + | 0.580721i | \(0.197229\pi\) | |||||||
\(860\) | 5.99017e7 | 2.76180 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.02272e7 | 1.38557 | ||||||||
\(863\) | 6.90619e6 | − | 1.19619e7i | 0.315654 | − | 0.546729i | −0.663922 | − | 0.747802i | \(-0.731109\pi\) |
0.979576 | + | 0.201073i | \(0.0644427\pi\) | |||||||
\(864\) | 1.10847e7 | + | 1.91992e7i | 0.505171 | + | 0.874982i | ||||
\(865\) | −158594. | − | 274692.i | −0.00720685 | − | 0.0124826i | ||||
\(866\) | −2.66828e7 | + | 4.62160e7i | −1.20903 | + | 2.09410i | ||||
\(867\) | −3.79300e6 | −0.171370 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.32086e6 | −0.0593345 | ||||||||
\(870\) | −2.31576e6 | + | 4.01101e6i | −0.103728 | + | 0.179662i | ||||
\(871\) | −2.50965e6 | − | 4.34684e6i | −0.112090 | − | 0.194146i | ||||
\(872\) | −1.38469e7 | − | 2.39835e7i | −0.616682 | − | 1.06813i | ||||
\(873\) | −869178. | + | 1.50546e6i | −0.0385987 | + | 0.0668550i | ||||
\(874\) | −4.45460e7 | −1.97256 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 7.20160e7 | 3.17080 | ||||||||
\(877\) | −4.57920e6 | + | 7.93141e6i | −0.201044 | + | 0.348218i | −0.948865 | − | 0.315682i | \(-0.897767\pi\) |
0.747821 | + | 0.663900i | \(0.231100\pi\) | |||||||
\(878\) | 35396.2 | + | 61308.0i | 0.00154960 | + | 0.00268399i | ||||
\(879\) | −6.96458e6 | − | 1.20630e7i | −0.304035 | − | 0.526603i | ||||
\(880\) | −2.52751e7 | + | 4.37777e7i | −1.10024 | + | 1.90566i | ||||
\(881\) | 2.45789e7 | 1.06690 | 0.533449 | − | 0.845833i | \(-0.320896\pi\) | ||||
0.533449 | + | 0.845833i | \(0.320896\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.10185e7 | −0.475575 | −0.237787 | − | 0.971317i | \(-0.576422\pi\) | ||||
−0.237787 | + | 0.971317i | \(0.576422\pi\) | |||||||
\(884\) | −1.62106e7 | + | 2.80776e7i | −0.697699 | + | 1.20845i | ||||
\(885\) | −969564. | − | 1.67933e6i | −0.0416120 | − | 0.0720740i | ||||
\(886\) | 7.92053e6 | + | 1.37188e7i | 0.338977 | + | 0.587125i | ||||
\(887\) | −1.43491e7 | + | 2.48534e7i | −0.612374 | + | 1.06066i | 0.378466 | + | 0.925615i | \(0.376452\pi\) |
−0.990839 | + | 0.135047i | \(0.956882\pi\) | |||||||
\(888\) | −5.41220e7 | −2.30325 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 3.23433e7 | 1.36870 | ||||||||
\(891\) | 569150. | − | 985797.i | 0.0240178 | − | 0.0416000i | ||||
\(892\) | 9.17924e6 | + | 1.58989e7i | 0.386273 | + | 0.669045i | ||||
\(893\) | −76640.9 | − | 132746.i | −0.00321612 | − | 0.00557048i | ||||
\(894\) | −1.40854e7 | + | 2.43966e7i | −0.589419 | + | 1.02090i | ||||
\(895\) | −1.50976e7 | −0.630013 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.11065e6 | −0.253575 | ||||||||
\(898\) | −1.05252e7 | + | 1.82302e7i | −0.435551 | + | 0.754397i | ||||
\(899\) | 907895. | + | 1.57252e6i | 0.0374659 | + | 0.0648929i | ||||
\(900\) | −2.86092e6 | − | 4.95525e6i | −0.117733 | − | 0.203920i | ||||
\(901\) | −1.38418e7 | + | 2.39747e7i | −0.568041 | + | 0.983876i | ||||
\(902\) | 3.41966e7 | 1.39948 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.02679e7 | 0.417889 | ||||||||
\(905\) | −1.53374e7 | + | 2.65651e7i | −0.622487 | + | 1.07818i | ||||
\(906\) | −1.00903e7 | − | 1.74768e7i | −0.408396 | − | 0.707363i | ||||
\(907\) | 7.78185e6 | + | 1.34786e7i | 0.314098 | + | 0.544033i | 0.979245 | − | 0.202679i | \(-0.0649647\pi\) |
−0.665148 | + | 0.746712i | \(0.731631\pi\) | |||||||
\(908\) | 5.58285e7 | − | 9.66979e7i | 2.24720 | − | 3.89226i | ||||
\(909\) | 1.18206e7 | 0.474491 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.36784e7 | 0.945273 | 0.472637 | − | 0.881257i | \(-0.343302\pi\) | ||||
0.472637 | + | 0.881257i | \(0.343302\pi\) | |||||||
\(912\) | 4.29683e7 | − | 7.44232e7i | 1.71065 | − | 2.96293i | ||||
\(913\) | 5.52801e6 | + | 9.57480e6i | 0.219479 | + | 0.380148i | ||||
\(914\) | 4.16432e7 | + | 7.21282e7i | 1.64884 | + | 2.85588i | ||||
\(915\) | 4.47445e6 | − | 7.74998e6i | 0.176680 | − | 0.306019i | ||||
\(916\) | −2.27406e7 | −0.895495 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −8.14963e6 | −0.319177 | ||||||||
\(919\) | −6.59343e6 | + | 1.14202e7i | −0.257527 | + | 0.446050i | −0.965579 | − | 0.260111i | \(-0.916241\pi\) |
0.708052 | + | 0.706160i | \(0.249574\pi\) | |||||||
\(920\) | 4.15756e7 | + | 7.20110e7i | 1.61945 | + | 2.80498i | ||||
\(921\) | −673491. | − | 1.16652e6i | −0.0261627 | − | 0.0453151i | ||||
\(922\) | 4.45117e7 | − | 7.70964e7i | 1.72443 | − | 2.98681i | ||||
\(923\) | −1.05649e7 | −0.408188 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.66158e6 | 0.255990 | ||||||||
\(926\) | 3.71702e7 | − | 6.43807e7i | 1.42452 | − | 2.46734i | ||||
\(927\) | −6.70796e6 | − | 1.16185e7i | −0.256384 | − | 0.444070i | ||||
\(928\) | 1.12235e7 | + | 1.94396e7i | 0.427817 | + | 0.741000i | ||||
\(929\) | −1.18400e7 | + | 2.05076e7i | −0.450105 | + | 0.779605i | −0.998392 | − | 0.0566850i | \(-0.981947\pi\) |
0.548287 | + | 0.836290i | \(0.315280\pi\) | |||||||
\(930\) | −1.54356e7 | −0.585216 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.41865e7 | −0.534979 | ||||||||
\(933\) | 659192. | − | 1.14175e6i | 0.0247918 | − | 0.0429406i | ||||
\(934\) | −1.66441e7 | − | 2.88284e7i | −0.624300 | − | 1.08132i | ||||
\(935\) | −5.40138e6 | − | 9.35546e6i | −0.202058 | − | 0.349974i | ||||
\(936\) | 9.65281e6 | − | 1.67192e7i | 0.360134 | − | 0.623770i | ||||
\(937\) | 9.81602e6 | 0.365247 | 0.182623 | − | 0.983183i | \(-0.441541\pi\) | ||||
0.182623 | + | 0.983183i | \(0.441541\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.86501e6 | 0.106038 | ||||||||
\(940\) | −217897. | + | 377408.i | −0.00804324 | + | 0.0139313i | ||||
\(941\) | 1.66086e7 | + | 2.87669e7i | 0.611446 | + | 1.05906i | 0.990997 | + | 0.133885i | \(0.0427453\pi\) |
−0.379551 | + | 0.925171i | \(0.623921\pi\) | |||||||
\(942\) | 2.36629e7 | + | 4.09853e7i | 0.868841 | + | 1.50488i | ||||
\(943\) | 1.71740e7 | − | 2.97463e7i | 0.628917 | − | 1.08932i | ||||
\(944\) | −1.61664e7 | −0.590452 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.00262e7 | −0.727563 | ||||||||
\(947\) | −3.69552e6 | + | 6.40082e6i | −0.133906 | + | 0.231932i | −0.925179 | − | 0.379531i | \(-0.876085\pi\) |
0.791273 | + | 0.611463i | \(0.209419\pi\) | |||||||
\(948\) | −3.19207e6 | − | 5.52883e6i | −0.115359 | − | 0.199808i | ||||
\(949\) | −1.49538e7 | − | 2.59007e7i | −0.538995 | − | 0.933568i | ||||
\(950\) | −8.66119e6 | + | 1.50016e7i | −0.311364 | + | 0.539299i | ||||
\(951\) | 1.94933e7 | 0.698930 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.81495e7 | −0.647341 | −0.323671 | − | 0.946170i | \(-0.604917\pi\) | ||||
−0.323671 | + | 0.946170i | \(0.604917\pi\) | |||||||
\(954\) | 1.25538e7 | − | 2.17439e7i | 0.446587 | − | 0.773511i | ||||
\(955\) | −6.34770e6 | − | 1.09945e7i | −0.225220 | − | 0.390093i | ||||
\(956\) | −7.03799e7 | − | 1.21902e8i | −2.49060 | − | 4.31385i | ||||
\(957\) | 576277. | − | 998141.i | 0.0203400 | − | 0.0352300i | ||||
\(958\) | 3.81354e7 | 1.34250 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.06904e8 | −3.74381 | ||||||||
\(961\) | 1.12888e7 | − | 1.95528e7i | 0.394311 | − | 0.682967i | ||||
\(962\) | 1.71169e7 | + | 2.96474e7i | 0.596332 | + | 1.03288i | ||||
\(963\) | −8.70946e6 | − | 1.50852e7i | −0.302639 | − | 0.524187i | ||||
\(964\) | −1.08518e7 | + | 1.87959e7i | −0.376105 | + | 0.651433i | ||||
\(965\) | 3.80498e6 | 0.131533 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.12321e7 | 1.07408 | 0.537038 | − | 0.843558i | \(-0.319543\pi\) | ||||
0.537038 | + | 0.843558i | \(0.319543\pi\) | |||||||
\(968\) | −4.48117e7 | + | 7.76162e7i | −1.53710 | + | 2.66234i | ||||
\(969\) | 9.18248e6 | + | 1.59045e7i | 0.314160 | + | 0.544140i | ||||
\(970\) | −7.48120e6 | − | 1.29578e7i | −0.255295 | − | 0.442184i | ||||
\(971\) | 6.83554e6 | − | 1.18395e7i | 0.232662 | − | 0.402982i | −0.725929 | − | 0.687770i | \(-0.758590\pi\) |
0.958591 | + | 0.284788i | \(0.0919232\pi\) | |||||||
\(972\) | 5.50177e6 | 0.186783 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −6.61558e7 | −2.23445 | ||||||||
\(975\) | −1.18811e6 | + | 2.05787e6i | −0.0400263 | + | 0.0693275i | ||||
\(976\) | −3.73034e7 | − | 6.46114e7i | −1.25350 | − | 2.17112i | ||||
\(977\) | −2.49513e7 | − | 4.32170e7i | −0.836291 | − | 1.44850i | −0.892975 | − | 0.450107i | \(-0.851386\pi\) |
0.0566835 | − | 0.998392i | \(-0.481947\pi\) | |||||||
\(978\) | −2.95536e7 | + | 5.11883e7i | −0.988013 | + | 1.71129i | ||||
\(979\) | −8.04866e6 | −0.268390 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.27758e6 | −0.108738 | ||||||||
\(982\) | 3.07611e6 | − | 5.32797e6i | 0.101794 | − | 0.176312i | ||||
\(983\) | 1.10831e7 | + | 1.91965e7i | 0.365828 | + | 0.633633i | 0.988909 | − | 0.148525i | \(-0.0474525\pi\) |
−0.623081 | + | 0.782158i | \(0.714119\pi\) | |||||||
\(984\) | 5.42586e7 | + | 9.39786e7i | 1.78641 | + | 3.09415i | ||||
\(985\) | 1.42618e7 | − | 2.47022e7i | 0.468365 | − | 0.811232i | ||||
\(986\) | −8.25169e6 | −0.270303 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.62622e7 | −2.15960 | ||||||||
\(989\) | −1.00575e7 | + | 1.74200e7i | −0.326962 | + | 0.566315i | ||||
\(990\) | 4.89880e6 | + | 8.48497e6i | 0.158855 | + | 0.275145i | ||||
\(991\) | 2.09458e7 | + | 3.62791e7i | 0.677504 | + | 1.17347i | 0.975730 | + | 0.218976i | \(0.0702718\pi\) |
−0.298226 | + | 0.954495i | \(0.596395\pi\) | |||||||
\(992\) | −3.74049e7 | + | 6.47872e7i | −1.20684 | + | 2.09031i | ||||
\(993\) | −2.28911e7 | −0.736704 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.68592e7 | 0.539856 | ||||||||
\(996\) | −2.67187e7 | + | 4.62781e7i | −0.853427 | + | 1.47818i | ||||
\(997\) | −2.11521e7 | − | 3.66364e7i | −0.673930 | − | 1.16728i | −0.976780 | − | 0.214243i | \(-0.931272\pi\) |
0.302851 | − | 0.953038i | \(-0.402062\pi\) | |||||||
\(998\) | 3.13794e7 | + | 5.43508e7i | 0.997284 | + | 1.72735i | ||||
\(999\) | −3.20269e6 | + | 5.54722e6i | −0.101531 | + | 0.175858i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 147.6.e.p.79.6 | 12 | ||
7.2 | even | 3 | 147.6.a.o.1.1 | yes | 6 | ||
7.3 | odd | 6 | 147.6.e.q.67.6 | 12 | |||
7.4 | even | 3 | inner | 147.6.e.p.67.6 | 12 | ||
7.5 | odd | 6 | 147.6.a.n.1.1 | ✓ | 6 | ||
7.6 | odd | 2 | 147.6.e.q.79.6 | 12 | |||
21.2 | odd | 6 | 441.6.a.ba.1.6 | 6 | |||
21.5 | even | 6 | 441.6.a.bb.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
147.6.a.n.1.1 | ✓ | 6 | 7.5 | odd | 6 | ||
147.6.a.o.1.1 | yes | 6 | 7.2 | even | 3 | ||
147.6.e.p.67.6 | 12 | 7.4 | even | 3 | inner | ||
147.6.e.p.79.6 | 12 | 1.1 | even | 1 | trivial | ||
147.6.e.q.67.6 | 12 | 7.3 | odd | 6 | |||
147.6.e.q.79.6 | 12 | 7.6 | odd | 2 | |||
441.6.a.ba.1.6 | 6 | 21.2 | odd | 6 | |||
441.6.a.bb.1.6 | 6 | 21.5 | even | 6 |